A297158 - OEIS

%I #10 Jan 02 2023 12:30:54

%S 0,1,0,1,2,1,0,1,2,3,4,3,2,3,4,5,6,5,4,3,2,1,0,1,2,1,0,-1,-2,-1,0,1,2,

%T 3,4,5,6,5,4,3,2,3,4,3,2,1,0,1,2,3,4,5,6,5,4,3,2,1,0,-1,-2,-1,0,1,2,3,

%U 4,3,2,1,0,1,2,3,4,5,6,5,4,3,2,1,0,1,2,3,4,5,6,5,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1

%N Ludic ladder sequence: a(n) = Sum_{k=1..n} (-1)^LudicPi(k), where LudicPi(n) = A192512(n)-1 gives the number of Ludic numbers > 1 and <= n.

%C This is an analogous sequence to A065358, but involving Ludic numbers (A003309) instead of primes. Compare the scatter-plots.

%H Antti Karttunen, <a href="/A297158/b297158.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="http://list.seqfan.eu/oldermail/seqfan/2018-February/018338.html">Discussion of SeqFan-list</a>, February 2018.

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(n) = Sum_{k=1..n} (-1)^(A192512(k)-1).

%o (Scheme, with memoization-macro definec)

%o (definec (A297158 n) (if (zero? n) n (+ (expt -1 (+ -1 (A192512 n))) (A297158 (- n 1)))))

%Y Cf. A003309, A192512.

%Y Differs from A065358 for the first time at n=19, where a(19) = 3, while A065358(19) = 5.

%K sign

%O 0,5

%A _Antti Karttunen_, Feb 22 2018